ALGEBRA 2/TRIGONOMETRY

Transcription

1 ALGEBRA 2/TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Friday, January 29, :15 a.m. to 12:15 p.m., only The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you. Notice... Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 39 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except for graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The formu1as that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions. or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration. A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. Al:IJ.31/\10N08U:UJG Vl:l8381V

2 Part I Answer all 27 questions in this part. Each correct answer will receive 2 credits. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet. [54] I A survey is to be conducted in a small upstate village to determine whether or not local residents should fund construction of a skateboard park by raising taxes. Which segment of the population would provide the most unbiased responses? (1) a club of local skateboard enthusiasts (2) senior citizens living on fixed incomes ( 3) a group opposed to any increase in taxes ( 4) every tenth person 18 years of age or older walking down Main St. Use this space for computations. 2 Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position? (1) -300 (2) -50 (3) 280 (4) The expression (1) 3 2 (2) 3x + y 2xy l_ +1- x y 2 xy is equivalent to (3) 3xy 2 (4) 3x + y 2 Algebra 2ffrigonometry - Jan. '16 [2]

3 4 Which relation does not represent a function? Use this space for computations. Domain Range Domain Range (1) (3) Domain Range Domain Range (2) (4) 5 In the diagram below, the spinner is divided into eight equal regions. Which expression represents the probability of the spinner landing on B exactly three times in five spins? (1) 8C 3 (i)3(~)5 (2) 8C 3 (i)5(~)3 (3) 5C3(~)2(~)3 (4) 5C3(~)3(~)2 Algebra 2ffrigonometry - Jan. '16 [3] [OVER]

4 6 The expression ~21a- 6b3c 2 is equivalent to Use this space for computations. 2 (1) 3bc3 a2 (3) 3b 6 c 5 a3 -- 3b 9 c 6 9J3:2 (2) (4) 3b al8 a2 7 The amount of money in an account can be determined by the formula A = Pert, where Pis the initial investment, r is the annual interest rate, and t is the number of years the money was invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest compounded continuously? (1) $ (2) $ (3) $10, (4) $10, x 1 8 What is x _ 1-2 _ 2x expressed as a single fraction? (1) x + 1 x-l (2) 2x x 2x +l (3) 2(x -1) 2x-l (4 ) 2(x-l) Algebra 2ffrigonometry - Jan. '16 [4]

5 9 What is the total number of points of intersection of the graphs of the equations 2x 2 - y 2 = 8 and y = x + 2? ( 1) 1 (2) 2 (3) 3 (4) 0 Use this space for computations. 10 Given the sequence: x, (x + y), (x + 2y),... Which expression can be used to determine the common difference of this sequence? (1) x - (x + y) (3) x (x + y) (2) (x + 2y) - (x + y) ( 4 ) (x + 2y) (x + y) 11 In a circle with a diameter of 24 cm, a central angle of 4 ; radians intercepts an arc. The length of the arc, in centimeters, is (1) 8rt (3) 16rt (2) 9rt (4) 32rt 12 Which graph is the solution to the inequality 4l2x < 27?,. D I I I 0 I (1) (2) II( I (3) (4) Algebra 2/Trigonometry - Jan. '16 [5] [OVER]

6 13 What is the sum of the roots of the equation -3x 2 + 6x - 2 = O? Use this space for computations. (1) _g_ (3) g_ 3 3 (2) 2 (4) The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. What is the expected number of students who had scores greater than 60? (1) 1.7 (3) 46 (2) 23 (4) If T = l0x 2, then log Tis equivalent to y (1) (1 + 2log x) - logy (2) log(l + 2x) - logy (3) (1-2log x) + logy (4) 2(1 - log x) +logy 16 Which statement regarding correlation is not true? ( 1) The closer the absolute value of the correlation coefficient is to one, the closer the data conform to a line. (2) A correlation coefficient measures the strength of the linear relationship between two variables. ( 3) A negative correlation coefficient indicates that there is a weak relationship between two variables. (4) A relation for which most of the data fall close to a line is considered strong. Algebra 2ffrigonometry - Jan. '16 [6]

7 3 17 What is the value of ~ cos ~1t? n=l Use this space for computations. (1) 1 (2) -1 (3) 0 (4) The roots of the equation 4(x 2-1) = -3x are ( 1) imaginary (2) real, rational, equal ( 3) real, rational, unequal (4) real, irrational, unequal 19 If f(x) = 2x 2-3x + 4, thenf(x + 3) is equal to (1) 2x 2-3x + 7 (3) 2x 2 + 9x + 13 (2) 2x 2-3x + 13 (4) 2x 2 + 9x The expression x(3i 2 ) 3 + 2xi 12 is equivalent to (1) 2x + 27xi (3) -25x (2) -7x (4) -29x 21 If the terminal side of angle 8 passes through the point (-3,-4), what is the value of sec 8? (1) 5 3 (2) 5 3 (3) 5 4 (4) _ji 4 Algebra 2ffrigonometry - Jan. '16 [7] [OVER]

8 22 When the inverse of tan 8 is sketched, its domain is (1) -1 :::; 8 ::; 1 (3) 0 < 8 <:rt Use this space for computations. (2) _lr < 8 < 1r (4) -oo < 8 < What is the third term of the recursive sequence below? a 1 = -6 1 an= 2an -1 - n (1) (2) (3) 1 2 (4) What is the equation of a circle with its center at (0, -2) and passing through the point (3, -5)? (1) x 2 + (y + 2) 2 = g (3) x 2 + (y + 2) 2 = 18 (2) (x + 2) 2 + y 2 = g (4) (x + 2) 2 + y 2 = If angles A and B are complementary, then sec B equals (1) csc(go 0 - B) (2) csc(b - go 0 ) (3) cos(b - go 0 ) (4) cos(go 0 - B) Algebra 2/I'rigonometry-Jan. '16 [8]

9 26 The legs of a right triangle are represented by x +.J2 and x -.J2. The length of the hypotenuse of the right triangle is represented by Use this space for computations. (1) ~2x (2) 2x (3) x.j2 + 2 (4) ~x What are the amplitude and the period of the graph represented by the equation y = -3cos ~? (1) amplitude: -3; period: ~ (2) amplitude: -3; period: fot (3) amplitude: 3; period: ~ ( 4) amplitude: 3; period: 6n Algebra 2ffrigonometry-Jan. '16 [9] [OVER]

10 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 28 Solve algebraically for x:.j2x = 8 Algebra 21frigonometry - Jan. '16 [10]

11 29 Factor completely: x 3 + 3x 2 + 2x + 6 Algebra 2ffrigonometry-Jan. '16 [11] [OVEF

12 30 Solve algebraically for the exact value of x: log 8 16 = x + 1 Algebra 2trrigonometry-Jan. '16 [12]

13 31 Determine how many eleven-letter arrangements can be formed from the word "CATTARAUGUS." Algebra 2ffrigonometry-Jan. '16 [13] [OVER]

14 32 Express -130 in radian measure, to the nearest hundredth. Algebra 2ffrigonometry - Jan. '16 [14]

15 33 Determine the area, to the nearest integer, of.6.sro shown below. A ~ s Algebra 2ffrigonometry - Jan. '16 [15] [OVER]

16 34 Prove that the equation shown below is an identity for all values for which the functions are defined: csc 8 sin 2 8 cot 8 = cos 8 Algebra 2/l'rigonometry-Jan. '16 [16]

17 35 Find the difference when ~ x 3 - ~ x 2 + ~ x is subtracted from 2x 3 + ~ x 2 - ~. Algebra 2ffrigonometry - Jan. '16 [17] [OVER]

18 Part III Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only I credit. All answers should he written in pen, except for graphs and drawings, which should he done in pencil. [ 12] 36 Find the exact roots of x 2 + lox - 8 = 0 by completing the square. Algebra 2ffrigonometry-Jan. '16 [18]

19 37 The table below gives the relationship between x and y. I : I Use exponential regression to find an equation for y as a function of x, rounding all values to the nearest hundredth. Using this equation, predict the value of x if y is , rounding to the nearest tenth. [Only an algebraic solution can receive full credit.] Algebra 2/Trigonometry - Jan. '16 [19] [OVER]

20 38 Solve the equation cos 2x = cos x algebraically for all values of x in the interval 0 :::; x < 360. Algebra 2/Trigonometry - Jan. '16 [20]

21 Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [ 6] 39 Given: DC = 10, AG = 15, BE = 6, FE = 10, mlabg = 40, mlgbd = 90, mlc < 90, BE ::: ED, and GF ::: FB A c D Find mla to the nearest tenth. Find BC to the nearest tenth. Algebra 2trrigonometry - Jan. '16 [21] [OVER]

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122 The State Education Department / The University of the State of New York Regents Examination in Algebra 2/Trigonometry January 2016 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) Raw Scale Raw Scale Raw Scale Raw Scale Score Score Score Score Score Score Score Score To determine the student s final examination score, find the student s total test raw score in the column labeled Raw Score and then locate the scale score that corresponds to that raw score. The scale score is the student s final examination score. Enter this score in the space labeled Scale Score on the student s answer sheet. Schools are not permitted to rescore any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam score. Schools are required to ensure that the raw scores have been added correctly and that the resulting scale score has been determined accurately. Because scale scores corresponding to raw scores in the conversion chart change from one administration to another, it is crucial that for each administration the conversion chart provided for that administration be used to determine the student s final score. The chart above is usable only for this administration of the Regents Examination in Algebra 2/Trigonometry. Algebra 2/Trigonometry Conversion Chart - Jan. '16 1 of 1